The alternating PBW basis for the positive part of the quantum affine sl2 algebra

par Prof. Paul Terwilliger (University of Wisconsin)

mercredi 22 mai 2019, 11:00 → 12:00 Europe/Paris

E1180 (Tours)

We discuss the positive part Uq^+ of the quantum affine sl2 algebra. The algebra Uq^+ has a presentation with two generators A, B that satisfy the cubic q-Serre relations. We introduce a PBW basis for Uq^+, said to be alternating. Each element of this PBW basis commutes with exactly one of A, B, qAB-q^{-1}BA. This gives three types of PBW basis elements; the  elements of each type mutually commute. We interpret the alternating PBW basis in terms of a q-shuffle algebra associated with affine sl2. We show how the alternating PBW basis is related to the PBW basis for Uq^+ found by Damiani in 1993. The alternating PBW basis is inspired by recent work of P. Baseilhac, K. Koizumi, K. Shigechi concerning boundary integrable systems with hidden symmetries.